CMS Note Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland

Available on CMS information server CMS NOTE 21/17 The Compact Muon Solenoid Experiment CMS Note Mailing address: CMS CERN, CH-1211 GENEVA 23, Switzerland 2 March 21 Study of a Level-3 Tau Trigger with the Pixel Detector D. Kotliński Paul Scherrer Inst., Villigen, Switzerland A. Nikitenko a) European Laboratory for Particle Physics (CERN), Switzerland R. Kinnunen Helsinki Institute of Physics, Helsinki, Finland Abstract We present a Monte Carlo study of the performance of a Level-3 Tau trigger based on the Pixel Detector data. The trigger is designed to select the Higgs bosons decaying into two τ leptons with τ jet(s) in the final state. The proposed trigger is particularly useful as it operates at an early stage of the CMS High Level Trigger system. The performance of the trigger is studied for the most difficult case of high luminosity LHC scenario. a) On leave from ITEP, Moscow

1 Introduction In this note we present a High Level Trigger algorithm to select τ-jets using data from the Pixel Detector only. This trigger is necessary to reduce the QCD background for the hadronic τ decays in particular in the 2 τ jet final state. The algorithm is assumed to be applied after the event selection with the Lvl-1 and Lvl-2 calorimeter Tau triggers [1] and [2], which will provide a region to search for isolated groups of tracks, well matched to the jet axis given by the calorimeter. The Pixel Detector data represents about 1 % of all tracker data [3], therefore the algorithm can be used at an early stage of the event selection with the tracker. The basic requirement of the tracker isolation criteria [4] is the reconstruction of low p t tracks with a good efficiency and an acceptable ghost rate rather than a precise measurement of transverse momenta. As we will show in this note these requirements can be reached thanks to the high granularity of the CMS Pixel Detector together with a robust track finding algorithm using pixel data only. 2 Pixel Detector simulation 2.1 Pixel Detector setup used in simulation The pixel detector configuration used in this simulation consists of three barrel layers located at mean radii 4.3 cm, 7.2 cm and 11. cm. The 52 cm long pixel barrel is supplemented by two endcap disks on each side (see Fig. 1). With this configuration the pixel detector provides 3 hit coverage up to rapidity η 2.2 (2 hit coverage up to 2.4). To enhance the spatial resolution by analog signal interpolation the use of charge sharing induced by the Figure 1: Perspective view of the CMS pixel detector. large charge drift (Lorentz angle 28 at 4T for electrons) is made. Hence the detectors are deliberately not tilted in the barrel layers but are tilted by 2 in the endcap disks resulting in a turbine like geometry. The pixel shape is 15*15 µm 2, which optimizes the position resolution in both the (r,φ) and the z coordinates, the pixel sensors are 25 µm thick (see Ref.[3] for more details). 2.2 Simulation of the detector response The pixel detector response was fully simulated with the CMSIM [7] (v.12) and ORCA [8] (v.44) software. During the pixel digitisation procedure the default value of the noise (35e) and the threshold (15e) were used. 2

The geometrical and threshold related pixel inefficiencies were present in the simulation but the random readout and bump-bonding inefficiencies were not simulated. The effect of hadronic reactions was also included. More details concerning the digitisation and clusterization procedure can be found in Ref. [3]. 3 Track and vertex reconstruction with Pixel Detector 3.1 Track reconstruction algorithm With 3 pixel hits one can reconstruct tracks using the pixel detector only. The algorithm used to find tracks has been explained in detail in Ref.[5], here only the most important details will be given. The three essential steps 7 cm 4 cm y ~ 1-3 y 7 cm 4 cm layer 2 layer 3 (,) x z (,) z layer 1 Figure 2: Pixel detector track finding algorithm to establish track candidates using the pixel detector are shown in Fig. 2. Pixel hit pairs from the first two layers (barrel+barrelor barrel+endcap) are matched in r φ and z r to establish track candidates. The cuts are optimized for a minimum track p t of 1 GeV and permit a maximum impact parameter in r φ of 1 mm. In the z r place the hit pairs have to point to a region in z within 3σ (+/- 15cm) of the LHC luminous region. Valid pixel pairs are matched with a 3 rd pixel hit, which can be either in the 3 rd barrel layer or in one of the endcap disks, forming a track candidate. Using these tracks a list of primary vertices (PV) is formed at z values where at least 3 tracks cross the z axis. Tracks which do not point to any PV candidate are erased. Due to the detector overlaps in the r φ direction for some Monte Carlo tracks more than one track candidate is found. To reduce this effect track pairs which share pixel hits and are closer than 1 mrads from each other are identified. A cleaning procedure then erases one of the tracks in each pair. For the event types discussed in this note the absolute track finding efficiency for tracks above 1 GeV is about 9%. Only reconstructed tracks which have all 3 hits correctly assigned are counted and the fraction is normalized to all Monte Carlo tracks which are within the full acceptance of the pixel detector (η 2). The algorithmic efficiency is between 93% and 95%, this fraction is normalized to the Monte Carlo tracks which have at least 3 pixel hits. The fraction of ghosts is between 5% and 8%, and is defined as the ratio of the number of reconstructed tracks having at least one hit wrongly assigned to all reconstructed tracks. All numbers presented above are for high luminosity events in the presence of 2 (on the average) minimum bias pile-up interactions. The track finding efficiency is illustrated for the τ-jet events in Fig. 3 where the number of reconstructed tracks vs. rapidity is compared to the number of Monte Carlo tracks. Only the signal tracks (those originating from the τ events) are plotted in the histogram. The difference between the solid line (reconstructed tracks) and the dashed line (Monte Carlo tracks with at least 3 hits) illustrates the algorithmic inefficiency. The difference between the dashed line and the dotted line (all MC tracks above 1 GeV) is due to tracks with less than 3 pixel hits. This can be caused by geometrical inefficiencies, far secondary vertices and other effects. Obviously the track parameters, fitted with 3 hits only, are much inferior to the full tracker resolution. The reconstructed track direction is satisfactory, with the resolution in the φ direction being 8 mrad and in the θ direction 11 mrad. The p t measurement however, is poor, mainly because of the small radius of the last hit (11 cm). For 2 GeV tracks this resolution is about 7%, but for 1 GeV tracks it reaches already 2% (see Ref.[5] for more details). The curvature of the tracks is sufficient to distinguish the track sign with 1% efficiency up to p t of 3-4 GeV. 3

h(5) ττ, high-luminosity Number of tracks/event.5.4.3.2.1-3 -2-1 1 2 3 Rapidity Figure 3: The reconstructed number of tracks per event versus rapidity for the τ jet events at the full LHC luminosity. Only the signal tracks having p t 1 GeV are drawn. The solid line shows the reconstructed tracks, the dashed line all Monte Carlo tracks ( 1 GeV ) with at least 3 pixel hits. The dotted line shows Monte Carlo tracks with at least 1 pixel hit. 4

3.2 Vertex reconstruction algorithm The primary vertex candidates found during the track finding stage are reanalyzed. Only PVs with at least 3 valid tracks are kept and the position of each vertex is estimated as the mean value of the z impact parameters of all tracks assigned to it. In addition to the main ( signal ) PV, 6 more PVs per event are found, on the average, at high luminosity. The signal PV can be usually found with a very high accuracy of about 5 µm. This is shown 6 5 4 3 2 1 -.4 -.3 -.2 -.1.1.2.3.4 MC vertex - Reco vertex. mm Figure 4: The difference in the positions of the Monte Carlo and reconstructed PVs for the τ jet events at high luminosity. in Fig. 4 where the difference in the z position of the reconstructed vertex and the Monte Carlo vertex is plotted. The inefficiency of this algorithm is low, for the event samples presented here only in less than 1% of events the signal PV is not found. 4 Eventsamples Higgs signal and QCD 2-jets background event samples have been generated with PYTHIA 6.152 [6]. Full detector simulation has been done with the CMSIM package [7] version 12 which includes the latest geometry of the Pixel Detector described in the chapter 2. Digitisation of the signal and background events with high luminosity pile-up superimposed has been performed with the ORCA package [8] version 44. Tracker digitisation has been done only for the events which have passed the Lvl-1 and Lvl-2 Tau trigger selections described in [2]. 4.1 Signal samples As the signal sample we have used SUSY Higgs events with the Higgs mass of 2 and 5 GeV, produced in association with a b b pair. The Higgs boson is required to decay into two τ leptons with both τ s decaying hadronically. Selection cuts requiring p τ jet t > 45 GeV and η τ jet < 2.4 were applied at the generator level. These requirements are much looser than those in the off-line analysis [9], which required at least two calorimetric jets with E t > 6 GeV within the tracker acceptance. 5

Lvl-2 τ-jet axis tr 1 signal cone R s p jet-track matching cone R m isolation cone R i p Figure5: A sketch showing the basic principleof the pixelτ-jet identification algorithm. 4.2 QCD background samples In Ref. [2] we have estimated that after the Lvl-1 and Lvl-2 Tau trigger selections of SUSY H ττ 2-jet channel the output QCD background rate is about 45 ± 4 (stat. error) events/second. About 92% of this rate (412 ev/s) is due to the QCD 2-jets events generated in the ˆp t bins of 5-8, 8-12, 17-23 GeV (77.2, 27.3 and 127.5 ev/s). Therefore, we first concentrate on the events from these 3 bins, trying to obtain the required rejection factor for events passing the Lvl-1 and Lvl-2 Tau trigger selections. 5 Lvl-3 Tau algorithm 5.1 Algorithm description and parameters The Lvl-3 pixel trigger algorithm is based on isolation cuts and is schematically shown in Fig 5. The τ-jet direction is defined by the Lvl-2 calorimeter trigger. All track candidates in a matching cone R m around the jet direction and above a p m t cut are considered in the search for signal tracks, that is tracks which originate from the hadronic τ decay. The track with the highest p t is declared the leading signal track (tr 1 in Fig 5). Any other track which is in the narrow signal cone R s around tr 1 is also assumed to come from the τ decay. A larger area R i is now searched for tracks above a p i t cut. If no tracks are found in the R i cone, except the ones which are already in the R s cone, the isolation criteria is fulfilled and the jet is labeled as a τ-jet. The narrow signal cone R s around the leading track tr 1 is needed in order to trigger on 3 prong tau decays in addition to 1 prong. Typical values of the cuts used above are : R s =.5, R m =.1, R i =.35, p s t =3 GeV and pi t =1 GeV. 5.2 Signal vertex identification The τ-jet algorithm mentioned above works very well at low-luminosity. At the high LHC luminosity, however, it s efficiency becomes small (about 5%) due to the large number of tracks originating from the pile-up interactions. The pixel detector comes to the rescue by being able to assign, in a unique way, each track to it s PV. The vertex of the leading track is assumed to be the signal PV. This assumption is correct for 99% of events, it fails only when 6

the highest p t track in the R m cone does not belong to the τ event. Once the signal PV is defined only those tracks which were assigned to it are considered in the isolation criteria. This approach increases the efficiency of our algorithm at high luminosity to the same value as at low luminosity ( 8%). 5.3 Choice of the isolation parameters Most of the parameters such as: matching cone size R m, signal cone size R s, p m t and p i t have been chosen, based on the Monte Carlo data, to be almost fully efficient for the τ jets from A/H ττ decays for the Higgs with M H 2 GeV. Fig. 6 shows the distance in the η, φ space between the Lvl-2 calorimeter τ jet axis and the leading p t track from τ decay both for 2 and 5 GeV Higgs bosons. According to this plot the matching cone size is chosen to be R m =.1. 6 5 4 3 2 1.2.4.6.8.1.12 R(Lvl-2 τ-jet - leading mc τ-track) 45 4 35 3 25 2 15 1 5.2.4.6.8.1.12 R max (leading mc τ-track - τ-track) Figure 6: The distance in η, φ space between the Lvl- 2 calorimeter τ jet axis and the leading p t track from the τ decay of a 2 GeV (empty histogram) and 5 GeV Higgs (full histogram). Figure 7: The distance in η, φ space between the leading p t track and others tracks in 3-prong τ decays for the Higgs mass of 2 GeV (empty histogram) and 5 GeV (full histogram). The size of the signal cone has been defined according to the requirement that it should contain all tracks from 3-prong decays of τ leptons. The distance in the η, φ space between the leading p t track and others tracks in the 3-prong τ decays is shown in Fig. 7 for the Higgs boson with the mass of 2 GeV and 5 GeV. The τ jets from the lower mass Higgs are produced with a softer E t spectrum, therefore the required signal cone size is bigger. For M H =5 GeV the signal cone of size R s =.5 contains all the 3 tracks, while for the M H =2 GeV a cone size of R s =.1 is needed. Since we would like to avoid any efficiency dependence on the Higgs mass the signal cone of R s =.1 has been chosen. The threshold on the reconstructed transverse momentum of the leading track in the signal cone (parameter p m t ) has been set to 3 GeV. For all other reconstructed tracks, both in the signal and the isolation cones, the threshold (parameter p i t ) has been set to pi t =1 GeV. These thresholds have been chosen by looking at the lowest possible kinematic limits of the corresponding Monte Carlo variables : p t of the leading τ-track (with maximal p t )and minimal p t of the tracks in 3-prong τ decays. Distributions for these variables are shown in Fig. 8 and Fig. 9 for τ jets from the Higgs with M H =5 GeV. 6 The performance of the Lvl-3 Tau algorithm Once the parameters R m, R s, p m t and p i t have been fixed, as described in the previous chapter, the only free parameter left is the size of the isolation cone R i. The variation of the QCD 2-jet background and the Higgs signal 7

1 9 8 7 6 5 4 3 2 1 1-1 1 1 1 2 mc max p t of τ-track 1 9 8 7 6 5 4 3 2 1 1-1 1 1 1 2 mc min p t of τ-track Figure 8: Transverse momentum of the leading τ track (with maximal p t ) from H ττ events with M H =5 GeV. Figure 9: Minimal p t of the tracks in 3-prong decays of τ leptons from H ττ events with M H =5 GeV. efficiency with the change of the isolation cone size is shown in Fig. 1 for Higgs mass of 2 GeV (full squares) and 5 GeV (full circles). The points from the left to the right correspond to the following values of R i =.5,.4,.35,.3 and.2. One can see that a rejection factor of 5 can be reached with an efficiency 75% which is in a good agreement with our previous off-line τ identification study [4]. It is important that the efficiency is almost independent of the Higgs mass. The same figure shows the efficiency also for a smaller value of the signal cone size R s =.5 (open squares and circles). It was shown in the previous chapter that a cone of this size does not always contain all tracks from 3 prong decays of τ leptons from the 2 GeV Higgs (see Fig. 7). In such a case τ tracks outside of the signal cone are counted as background tracks, which leads to a smaller efficiency for the 2 GeV Higgs as compared to the 5 GeV Higgs. A rejection factor of about 1 can be achieved for R s =.5 but with a different efficiency for the 5 GeV (75%) and 2 GeV (7%) Higgs. The dependence of the signal and background efficiencies on the signal cone size is shown in Fig. 11. For the values of R s.8-.1 the signal efficiency is the same for both Higgs masses while the background increases by about a factor of 2 in comparison to R s =.5. We obtain, within statistical errors, the same rejection factor for QCD 2-jet events for the three ˆp t bins analyzed in this note. The rejection factors are.18 ±.7,.21 ±.2 and.19 ±.2 for ˆp t bins of 5-8, 8-12 and 17-23 GeV respectively (for R m =.1, R s =.1, R i =.4, p m t =3 GeV, p i t=1 GeV). The track finding performance of our Lvl-3 Tau trigger is presented in the Tab. 1 and Tab. 2. Tab. 1 shows that in 1% of the Higgs (M H =5 GeV) events no tracks were found in the signal cone. This is explained by the internal inefficiency of the Pixel Detector as described in chapters 2 and 3. For the remaining events in 98% of the cases at least one τ track has been found in the signal cone. Table 1: Track finding performance of Lvl-3 Tau trigger for 5 signal Higgs events with M H =5 GeV (R m =.1, R s =.5, R i =.35, p m t =3 GeV, pi t =1 GeV). N of rec. tracks in a signal cone 1 2 3 4 5 N of events with a given number of rec. tracks 53 348 52 44 2 1 N of events with τ tracks n tr =1,3,5 or 7 (42,11,) (321,27,) (6,46,) (,43,1) (,1,1) (,1,) N of events where at least one rec. track is a τ-track 338 52 44 2 1 Tab. 2 presents the cases when exactly two tracks have been reconstructed in the signal cone. They are mainly 3 8

ε(h(2,5 GeV) ττ, τ 1,3h+X).9.85.8.75.7.65.6.55.5.5.1.15.2.25.3.35.4 ε(qcd bkg.) Figure 1: The variation of the QCD background and the Higgs signal efficiency as a function of the isolation cone size (.2,.3,.35,.4,.5) for Higgs mass 2 GeV (squares) and 5 GeV (circles) and for two values of the signal cone size.5 (full marks) and.1 (open marks). Other parameters are R m =.1, p m t =3 GeV and pi t =1 GeV. ε(h(2,5 GeV) ττ, τ 1,3h+X).8.78.76.74.72.7.68.66.64.62.6 Higgs 5 GeV v.s. qcd 8-12 GeV Higgs 2 GeV v.s. qcd 8-12 GeV R S.4.5.6.7.8.9.1.5.75.1.125.15.175.2.225.25 ε(qcd bkg.) Figure 11: The variation of the QCD background (ˆp t bin of 8-12 GeV) and the Higgs signal efficiency as a function of the signal cone size.4,.5,....1 for Higgs mass 2 GeV (squares) and 5 GeV (triangles). Other parameters are R i =.35, R m =.1, p m t =3 GeV and p i t=1 GeV. 9

prong τ decays where 2 τ tracks are found and the 3 rd one is lost. Interesting events are those where 2 τ tracks are reconstructed as one, or sometimes, one τ track is reconstructed as two. For the last case the cleaning procedure has been already applied as described in chapter 3 to reduce it. Such effects cannot be completely eliminated, however, in this case they do not degrade the Lvl-3 Tau trigger performance significantly. Table 2: Higgs signal events with M H =5 GeV, where exactly 2 tracks have been reconstructed in the signal cone (R m =.1, R s =.5, R i =.35, p m t =3 GeV, p i t=1 GeV). number of events number of MC τ-tracks tracks found in a signal cone 35 3 2 τ-tracks are found, 1 τ-track is lost 3 3 1 τ-track and 1 non τ-track are found, 2 τ-tracks are lost 8 3 3 τ-tracks are found but 2 τ-tracks are reconstructed as one 3 1 1 τ-track is reconstructed as 2 tracks 3 1 1 τ-track and 1 non τ-track are found 7 Summary and plans A Lvl-3 Tau trigger algorithm based on the pixel detector data is proposed. The algorithm performance has been studied for the most difficult case of the high luminosity and for the signal events of SUSY Higgs decaying into two τ leptons with both τ s decaying into hadrons. The algorithm is assumed to work after the Lvl-1 and Lvl-2 calorimeter Tau triggers, at an early stage of the further tracker selection. We have found that a rejection factor of about 5 can be achieved for the background QCD 2-jet events, which have passed the Lvl-1 and Lvl-2 Tau triggers. For this rejection factor the efficiency for the H ττ 2 jet events is 75% and doesn t depend on the Higgs mass for M H 2 GeV. A bigger rejection factor can be reached but with efficiency depending on the Higgs mass. For the rejection factor of 1 the efficiency is 75% for the Higgs with the mass of 5 GeV and 7% for the Higgs with the mass of 2 GeV. The performance of this Lvl-3 Tau trigger (efficiency vs. rejection factor) is comparable with our previous off-line τ jet identification studies. As was mentioned in chapter 4 the background rate reduction has been studied for QCD 2-jet events for the ˆp t bins 5-8, 8-12 and 17-23 GeV, which represent about 92 % of the total rate after Lvl-1 and Lvl-2 Tau triggers. Evaluation of the rate reduction for other ˆp t bins has still to be done. However we don t expect any degradation of the performance since (within statistical errors) the rejection factors are the same for all ˆp t bins used in this study. In the future we will investigate the final High Level Trigger selection for the H ττ 2 jet events by identifying the second τ jet present in event. We also plan to evaluate the performance of the Lvl-3 Tau trigger for the low luminosity running scenario when only 2 barrel pixel layers will be present. 8 Acknowledgments We would like to thank S. Eno, D. Denegri and P. Sphicas for the support of this work and useful discussions. We also would like to acknowledge all members of the CMS Software team for their help and advice. 1

References [1] The TriDAS Project. Technical Design Report. CERN/LHCC 2-38, CMS TDR 6.1, 15 December 2 [2] CMS Note 2/55, S. Eno, S. Dasu, R. Kinnunen, A. Nikitenko and W. Smith. [3] The Tracker Project. Technical Design Report. CERN/LHCC 98-6, CMS TDR 5, 15 April 1998 [4] CMS Note 1997/2, R. Kinnunen and A. Nikitenko [5] CMS Internal Note 2/22, D. Kotlinski. [6] http://www.thep.lu.se/ torbjorn/pythia.html [7] http://cmsdoc.cern.ch/cmsim/cmsim.html [8] http://cmsdoc.cern.ch/orca/ [9] CMS Note 1999/37, R. Kinnunen and D. Denegri 11